Flag-Transitive 2-Designs Arising from Line-Spreads in PG(2n - 1, 2)

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Abstract

A Singer cycle in GL(n, q) is an element of order qn - 1 permuting cyclically all the nonzero vectors. Let σ be a Singer cycle in GL(2n, 2). In this note we shall count the number of lines in PG(2n - 1, 2) whose orbit under the subgroup of index 3 in the Singer group 〈σ〉 is a spread. The lines constituting such a spread are permuted cyclically by the group 〈σ3〉, hence gives rise to a flag-transitive 2-(22n, 4, 1) design.

Original languageEnglish
Pages (from-to)209-213
Number of pages5
JournalGeometriae Dedicata
Volume77
Issue number2
DOIs
Publication statusPublished - 1999 Jan 1
Externally publishedYes

Keywords

  • Affine space
  • Flag-transitive design
  • Projective space
  • Singer cycle

ASJC Scopus subject areas

  • Geometry and Topology

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